TODAY IN SCIENCE HISTORY ®  •  TODAYINSCI ®
Celebrating 25 Years on the Web
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “Environmental extremists ... wouldn�t let you build a house unless it looked like a bird�s nest.”
more quiz questions >>
Home > Category Index for Science Quotations > Category Index I > Category: Invariance

Invariance Quotes (4 quotes)

Amid all the revolutions of the globe, the economy of Nature has been uniform, ... and her laws are the only things that have resisted the general movement. The rivers and the rocks, the seas and the continents, have been changed in all their parts; but the laws which direct those changes, and the rules to which they are subject, have remained invariably the same.
Illustrations of the Huttonian Theory of the Earth (1802) collected in The Works of John Playfair (1822), Vol. 1, 415
Science quotes on:  |  Change (639)  |  Continent (79)  |  Direct (228)  |  General (521)  |  Invariably (35)  |  Law (913)  |  Movement (162)  |  Nature (2017)  |  Remain (355)  |  Revolution (133)  |  River (140)  |  Rock (176)  |  Rule (307)  |  Sea (326)  |  Subject (543)  |  Thing (1914)

The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. That such is the case a few indications will suffice to show. The mathematical concepts of constant and variable are represented familiarly in life by the notions of fixedness and change. The concept of equation or that of an equational system, imposing restriction upon variability, is matched in life by the concept of natural and spiritual law, giving order to what were else chaotic change and providing partial freedom in lieu of none at all. What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an “ever flying perfect” as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration. The supreme concept of functionality finds its correlate in life in the all-pervasive sense of interdependence and mutual determination among the elements of the world. What is known in mathematics as transformation—that is, lawful transfer of attention, serving to match in orderly fashion the things of one system with those of another—is conceived in life as a process of transmutation by which, in the flux of the world, the content of the present has come out of the past and in its turn, in ceasing to be, gives birth to its successor, as the boy is father to the man and as things, in general, become what they are not. The mathematical concept of invariance and that of infinitude, especially the imposing doctrines that explain their meanings and bear their names—What are they but mathematicizations of that which has ever been the chief of life’s hopes and dreams, of that which has ever been the object of its deepest passion and of its dominant enterprise, I mean the finding of the worth that abides, the finding of permanence in the midst of change, and the discovery of a presence, in what has seemed to be a finite world, of being that is infinite? It is needless further to multiply examples of a correlation that is so abounding and complete as indeed to suggest a doubt whether it be juster to view mathematics as the abstract idealization of life than to regard life as the concrete realization of mathematics.
In 'The Humanization of Teaching of Mathematics', Science, New Series, 35, 645-46.
Science quotes on:  |  Abide (12)  |  Abound (17)  |  Abstract (141)  |  Approximate (25)  |  Aspiration (35)  |  Attain (126)  |  Attention (196)  |  Bear (162)  |  Become (821)  |  Being (1276)  |  Belief (615)  |  Birth (154)  |  Boy (100)  |  Build (211)  |  Call (781)  |  Case (102)  |  Cease (81)  |  Central (81)  |  Change (639)  |  Chaotic (2)  |  Chief (99)  |  Cold (115)  |  Complete (209)  |  Conceive (100)  |  Concept (242)  |  Concrete (55)  |  Constant (148)  |  Content (75)  |  Correlate (7)  |  Correlation (19)  |  Deal (192)  |  Deep (241)  |  Detach (5)  |  Determination (80)  |  Discovery (837)  |  Doctrine (81)  |  Dominant (26)  |  Doubt (314)  |  Dream (222)  |  Element (322)  |  Ralph Waldo Emerson (161)  |  Enterprise (56)  |  Equation (138)  |  Especially (31)  |  Estate (5)  |  Everywhere (98)  |  Example (98)  |  Excellence (40)  |  Explain (334)  |  Far (158)  |  Fashion (34)  |  Father (113)  |  Figure (162)  |  Find (1014)  |  Finite (60)  |  Fixed (17)  |  Flux (21)  |  Fly (153)  |  Flying (74)  |  Freedom (145)  |  Functionality (2)  |  General (521)  |  Give (208)  |  Gray (9)  |  Great (1610)  |  Guise (6)  |  Handle (29)  |  High (370)  |  Hope (321)  |  Human (1512)  |  Idea (881)  |  Ideal (110)  |  Idealization (3)  |  Impose (22)  |  Indeed (323)  |  Indication (33)  |  Infinite (243)  |  Infinitude (3)  |  Interdependence (4)  |  Interest (416)  |  Know (1538)  |  Known (453)  |  Law (913)  |  Lawful (7)  |  Life (1870)  |  Limit (294)  |  Man (2252)  |  Match (30)  |  Mathematics (1395)  |  Mean (810)  |  Meaning (244)  |  Meanings (5)  |  Midst (8)  |  Mistake (180)  |  Most (1728)  |  Multiply (40)  |  Must (1525)  |  Mutual (54)  |  Name (359)  |  Natural (810)  |  Nature Of Mathematics (80)  |  Nearer (45)  |  Needless (4)  |  Never (1089)  |  Notion (120)  |  Object (438)  |  Order (638)  |  Orderly (38)  |  Painting (46)  |  Partial (10)  |  Passion (121)  |  Past (355)  |  Perfect (223)  |  Permanence (26)  |  Pervasive (6)  |  Poetry (150)  |  Precisely (93)  |  Presence (63)  |  Present (630)  |  Problem (731)  |  Process (439)  |  Provide (79)  |  Pure (299)  |  Rationality (25)  |  Realization (44)  |  Regard (312)  |  Represent (157)  |  Restriction (14)  |  Rock (176)  |  Roll (41)  |  Save (126)  |  Scene (36)  |  Sculpture (12)  |  Seem (150)  |  Sense (785)  |  Serve (64)  |  Serving (15)  |  Show (353)  |  Space (523)  |  Spiritual (94)  |  Stately (12)  |  Static (9)  |  Successor (16)  |  Suffice (7)  |  Suggest (38)  |  Supreme (73)  |  System (545)  |  Thing (1914)  |  Through (846)  |  Time (1911)  |  Time And Space (39)  |  Transfer (21)  |  Transformation (72)  |  Transmutation (24)  |  Tumble (3)  |  Turn (454)  |  Unto (8)  |  Variability (5)  |  Variable (37)  |  View (496)  |  Will (2350)  |  World (1850)  |  Worth (172)

The fundamental biological variant is DNA. That is why Mendel's definition of the gene as the unvarying bearer of hereditary traits, its chemical identification by Avery (confirmed by Hershey), and the elucidation by Watson and Crick of the structural basis of its replicative invariance, are without any doubt the most important discoveries ever made in biology. To this must be added the theory of natural selection, whose certainty and full significance were established only by those later theories.
In Jacques Monod and Austryn Wainhouse (trans.), Chance and Necessity: An Essay on the Natural Philosophy of Modern Biology (1971), 104.
Science quotes on:  |  Oswald Avery (6)  |  Basis (180)  |  Biological (137)  |  Biology (232)  |  Certainty (180)  |  Chemical (303)  |  Confirm (58)  |  Confirmation (25)  |  Francis Crick (62)  |  Definition (238)  |  Discovery (837)  |  DNA (81)  |  Doubt (314)  |  Elucidation (7)  |  Fundamental (264)  |  Gene (105)  |  Heredity (62)  |  Identification (20)  |  Importance (299)  |  Gregor Mendel (22)  |  Most (1728)  |  Must (1525)  |  Natural (810)  |  Natural Selection (98)  |  Replication (10)  |  Selection (130)  |  Significance (114)  |  Structural (29)  |  Structure (365)  |  Theory (1015)  |  Trait (23)  |  Variant (9)  |  James Watson (33)  |  Why (491)

Wheeler’s First Moral Principle: Never make a calculation until you know the answer. Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every paradox and puzzle. Courage: No one else needs to know what the guess is. Therefore make it quickly, by instinct. A right guess reinforces this instinct. A wrong guess brings the refreshment of surprise. In either case life as a spacetime expert, however long, is more fun!
In E.F. Taylor and J.A. Wheeler, Spacetime Physics (1992), 20.
Science quotes on:  |  Answer (389)  |  Argument (145)  |  Bring (95)  |  Calculation (134)  |  Case (102)  |  Conservation (187)  |  Courage (82)  |  Derivation (15)  |  Estimate (59)  |  Expert (67)  |  First (1302)  |  Fun (42)  |  Guess (67)  |  Instinct (91)  |  Know (1538)  |  Know The Answer (9)  |  Knowledge (1647)  |  Life (1870)  |  Long (778)  |  Moral (203)  |  More (2558)  |  Need (320)  |  Never (1089)  |  Paradox (54)  |  Physical (518)  |  Physics (564)  |  Principle (530)  |  Puzzle (46)  |  Quickly (21)  |  Refreshment (3)  |  Reinforce (5)  |  Reinforcement (2)  |  Right (473)  |  Simple (426)  |  Spacetime (4)  |  Surprise (91)  |  Symmetry (44)  |  Try (296)  |  Wrong (246)


Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
Thank you for sharing.
- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton


by Ian Ellis
who invites your feedback
Thank you for sharing
on Blue Sky.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.